Let a and b be real numbers such that a^3+3ab^2=679 and 3a^2*b+b^3=-679. Find a+b.
CPhill's awesome answer:
a^3 + 3ab^2 = 679
3a^2b + b^3 = -652
Note that ( a + b)^3 = ( a^3 + 3a^2b) + (3ab^2 + b^2) = (a^3 + 3ab^2 ) + ( 3a^2b + b^3)
So
( a + b)^3 = 679 - 652
(a + b)^3 = 27 take the cube root of both sides
(a + b) = 3
